Correlation between microstructure and yield strength of as-quenched and Q&P steels with different carbon content (0.06–0.42 wt%C)

Abstract

Quenching and partitioning (Q&P) steels have been attracted much attention due to excellent combination of strength and ductility. However, the actual Q&P microstructures may contain the carbon-depleted martensite (i.e., initial martensite, M₁), bainitic ferrite (BF), secondary martensite (M₂) and retained austenite (RA). Hence, it is challenging to build a quantitative model of the yield strength of Q&P microstructures, since it requires prior knowledge of the yield strength of each constituent phase that is not always in a clear state in Q&P microstructures. In the present work, based on the analysis with respect of microstructural heterogeneities inevitably existing during martensitic transformation, both as-quenched and Q&P microstructures are simplified and regarded as a mixture of α′ phase (containing M₁, M₂ or BF) and γ phase (RA). The carbon content, dislocation density and substructure size of the α′ phase and γ phase were measured by SEM, EBSD and XRD. Then we build two generalized physical models to predict the yield strength of as-quenched and Q&P steels with the carbon content in range of 0.06–0.42 wt%. The physical models show the yield strength of α′ phase varies as the reciprocal of the square root of the block width (Hall-Petch relation), but varies as the inverse of the lath thickness (Langford-Cohen relation). The deviation analysis indicates that the assumption and simplification with regard of microstructure do not greatly affect the accuracy of the prediction of yield strength for both as-quenched and Q&P steels, with uncertainty less than 10%. The effect of carbon content and microstructural features on the yield strength of as-quenched and Q&P steels was discussed in terms of the developed physical models. It reveals that the residual carbon atom in α’ phase is still the dominant factor controlling the yield strength of Q&P steels, despite of possible highly uneven carbon distribution.

Introduction

The third-generation AHSSs have been ongoing to increase strength and ductility to higher levels with the goal of decreasing the weight of steel components [[1], [2], [3], [4]]. In this context, the quenching and partitioning (Q&P) process has been proposed by J. Speer et al. to obtain an excellent combination of strength and ductility in lean alloy steels [5,6]. The Q&P concepts involves an initial quenching step to a quenching temperature (T_q) between the martensite-start temperature (M_s) and the martensite-finish temperature (M_f), followed by an isothermal holding at T_q (or higher than T_q) with the purpose of promoting carbon partitioned from martensite into austenite, thereby obtaining more retained austenite at room temperature [6]. The ideal microstructures of Q&P steels consist of carbon-enriched retained austenite and carbon-depleted martensite. In fact, the bainitic ferrite may form during the partitioning step, and secondary martensite may form during the final quenching step if the carbon enrichment in austenite is not sufficient [7,8]. Hence, the actual Q&P microstructures are very complex, which may contain the carbon-depleted martensite (i.e., initial martensite, M₁), bainitic ferrite (BF), secondary martensite (M₂) and retained austenite (RA). On one hand, the transformation induced plasticity (TRIP) effect of the retained austenite has great contribution to strength and ductility through enhancing the work hardening capacity of the Q&P steels [9]. On the other hand, the martensite and bainite contribute to the increased strength due to the refined substructure and high dislocation density.

With development of materials genome idea, it is very essential to build the quantitative relationship between microstructure and mechanical properties of Q&P steels in order to design the process parameters better and faster. Most works in Q&P steels have focused on the relationship between retained austenite and ductility, and also on the mechanism of deformation [10,11]. Some research has just been carried out on the strengthening mechanism of Q&P microstructures until recently [3,12]. It is considered to be challenging to build a quantitative model of the yield strength of Q&P microstructures, since it requires prior knowledge of the yield strength of each constituent phase that is not always in a clear state in Q&P microstructures.

We begin with a brief overview of recent development in understanding strengthening mechanism of as-quenched lath martensite. It is suggested that the strength of martensitic microstructure is dominated by its carbon content [13]. The yield strength increases approximately linearly with carbon content up to about 0.5 wt% where martensite is mainly lath martensite, but the mechanism of this strengthening is still controversial. The experiment and strengthening mechanism of as-quenched Fe-Ni-C alloys have been explored [14]. Through designing subzero M_s temperatures and testing at subzero temperatures, any segregation of carbon atoms to dislocations or interfaces or retained austenite or the rearrangement of carbon into clusters was eliminated, in other words, the carbon atoms were ideally trapped in the set of octahedral sites of the martensite. This experiment provides a case for interstitial solid solution strengthening as the major strengthening mechanism of as-quenched martensite, and builds a relationship between yield strength (0.2% offset flow stress) and carbon content [13]:

$${\sigma }_{0.2}\left(\text{MPa}\right)=461+1310{x_{\text{C}}}^{1/2}$$

However, it is impossible to prevent carbon diffusion during quenching in the low alloy carbon steels with above-room temperature M_s. Many evidences have shown that most of carbon atoms (even up to 90%) are segregated to dislocation and lath boundaries or form Cottrell atmospheres [[15], [16], [17], [18], [19]]. Hence, it is suggested that the solid solution strengthening by carbon could not be the dominant contribution to strength. Norstrom [20] found that dislocation density within the lath martensite increases with carbon content and confirmed that the increased dislocation density dominates the yield strength rather than solid solution strengthening by carbon. Hence, it requires an accurate measurement of dislocation density of martensitic matrix to build the strengthening model. E.I. Galindo-Nava et al. [21] proposed a model to describe the lath width and dislocation density as a function of carbon content and successfully predicted the yield strength of low alloy martensitic and dual-phase steels under as-quenched and tempered conditions. Interestingly, B. Hutchinson et al. [18] confirmed that the strengthening contribution from segregated carbon atoms behave similarly to that from carbon in true solid solution.

The carbon diffusion from martensite into untransformed austenite is conscious and encouraged in the Q&P steels. The carbon content in initial martensite (M₁) is measured by 3D-APT and EPMA and is very low due to the carbon partitioning from martensite into austenite [3,8,22]. Although the secondary martensite (M₂) has relatively higher overall carbon content because it inherits the carbon from carbon-enriched but unstable austenite, the segregation of carbon atoms also exists in M₂ [3,23] (see Supplementary material). Meanwhile, the bainitic ferrite (BF) may form in Q&P steels [24]. The argument on the carbon content in BF has lasted for a long time [25]: one viewpoint is that the carbon content in BF is close to equilibrium solid solubility of carbon in ferrite (below 0.02 wt%); another viewpoint is that the carbon in BF is a little supersaturated. This uneven carbon distribution in each constituent phase brings about challenge to evaluating the effect of carbon content on yield strength of Q&P steels.

Besides the uneven carbon distribution, there are crystallographic and morphological heterogeneities in martensite, which are determined by the nature of martensitic transformation. L. Morsdorf et al. [26] reported the multi-scale characteristics of martensitic microstructures by a multi-probe methodology and found that the lath martensite contains both micron-sized coarse laths and nano-scaled thin laths. The early transformed coarse laths subjected to more extensive auto-tempering or auto-partitioning during quenching process have relatively lower dislocation density in comparison to the later transformed thinner laths. It suggested that the lath martensite should be regarded as a nano-composite structure with soft and hard phases. In this sense, the morphological heterogeneities are more obvious in Q&P microstructure, especially in case that it contains M₁ and M₂, which are determined by Q&P process parameters, such as initial quenching temperature (T_q) [3].

As mentioned above, both as-quenched and Q&P microstructures of low-alloy steels exhibit various degree of carbon distribution and morphological heterogeneities. In spite of this, it is noticed that these microstructural heterogeneities in lath martensite are not independent, such as the carbon distribution affects the dislocation density and vice-versa [27,28]; the dislocation density increases with the decrease of lath thickness [21,29], while the lath thickness is strongly related to carbon segregation and Cottrell atmosphere [21]. Hence, the strengthening contributions from carbon content, dislocation density and substructures might also be dependent, which provide a possibility to develop a generalized physical model to describe the yield strength of as-quenched or quenched & partitioned lath martensite.

Based on the concept, we assume that the M₁, M₂ as well as BF (if present) in Q&P microstructure are regarded as a single α′ phase with highly heterogeneous carbon distribution. The carbon content, dislocation density and grain size of the α’ phase were measured by SEM, EBSD and XRD. Then we build a generalized physical model to predict the yield strength of as-quenched and Q&P steels with 0.06–0.42 wt% C. The results show that the assumption and simplification with regard of microstructure do not greatly affect the accuracy of the prediction.